# Fairlead tensions of Test24 not matching with hand calculation in still conditions

Dear Jason

I have a doubt regarding the fairlead tensions of Test24 (OC3 Hywind Spar).

How I worked out is given below:
In my understanding Fairlead tension of a catenary mooring should be the product of suspended mooring line length with submerged weight per metre. The hand calculations I did are here.
Platform mass+tower-top mass+tower mass+mooring mass= (submerged volumerho)
mooring mass=(8029.21
1025)-(7466330.000+349389.844+249718.000)
mooring mass=164502.406
no. of lines=3
mooring mass per line=164502.406/3=54834.135 kg
The above mooring mass is till touchdown from fairlead(hang-off), as the rest is supported by seabed itself.

In still conditions (no wind, no wave and no rotation of wind turbine), the fairlead tensions output by FAST should match the above hand calcs. But when i simply ran Test24 with WaveMod=0 (still water), CompInflow=0 (no windflow), CompAero=0, CompServo=0, RotSpeed=0 (no rotation)…, I don’t see the tension matching with hand calcs

I used Moordyn module. I have used similar calculations for TLP for which the pretensions was matching with hand calculations. I’m doing this cross check to ensure my initial system setup.

I am attaching moordyn file here.
Could you please give suggestions where I would’ve gone wrong?
MoorDyn.txt (2.13 KB)

Dear Jay,

I haven’t checked all of your math, but your process refers only to the mooring pretension in the vertical direction. The horizontal mooring tension depends on geometry of the catenary line. The fairlead tension output by MoorDyn is the vector sum of the horizontal and vertical tensions. See Figure 5-3 in the OC3-Hywind specifications report for more information: nrel.gov/docs/fy10osti/47535.pdf.

Best regards,

Dear Jason,

You’re right. Really appreciate your quick support.

The initial tensions are getting closer to hand calculations only with stretched length input for UnstrLen in moordyn module. Could you please give any suggestions why is this so in moordyn module?

Many Thanks,

Dear Jay,

When you say, “the initial tensions are getting closer…”, do you mean that the final tensions (after start-up transients have died down) are correct regardless, but the tensions at time zero are only correct if you specify the stretched length in place of the unstretched length? Please clarify.

Best regards,

Dear Jason,

Yes, the final tensions (after start-up transients have died down) are correct (getting closer, not 100%), when I input stretched length for UnstrLen in moordyn module. For clarity I have presented the figure below.

I understand that the tensions in all mooring lines will not be 100% same, as the COG of tower-top mass is at some offset (OverHang given in Turbine Configuration of ElastoDyn module). Please correct me if my understanding is wrong.

I did hand calculations using catenary equations to get anchor co-ordinates to use in moordyn module. I couldn’t attach the excel file here, so adding screenshot.

Even with stretched length input in place of UnstrLen in moordyn module, I am getting slightly higher fairlead tensions (as shown in spar-mooring-3.PNG). There exists a small difference. Could you please tell how can I ensure my initial model setup is correct.

moor.txt (2.15 KB)
Thanks,

Dear Jay,

I’m not sure understand enough about what you are doing to answer, but here are a few comments:

• UnstrLen in MoorDyn should be set equal to the unstretched length of the mooring line, not the stretched length.
• *The tensions should not be the same between the 3 lines if the spar has displaced in any way (e.g. as a result of the overhanging weight of the rotor-nacelle-assembly).
• *I don’t know what theory you are using in your “hand calculation”, but does this calculation match the solution calculated by MAP++, which is solving the analytical quasi-static catenary equations?
• *I don’t know what each of the variables means in your spreadsheet, but from the data provided in the OC3-Hywind specifications report and corresponding MooringLineFD.txt file, the following values are reported at the undisplaced DISTANCE = 848.67 m (by linearly interpolating between 848.5 and 849.0 m):

TENSION = 911.1 kN
H.TENSION = 737.0 kN
SUSPL = 767.4 m. which corresponds to an unstretched length of line resting on the seabed = 134.8 m
TEN.ANCH = 737.0 kN

These values are a bit different than what you report in your spreadsheet and the result of your “hand calculation”.

Best regards,

Dear Jason,

I was under the impression that my hand calculations are correct (not 100%) as the values are closely matching with what is given in page 21 of “Definition of the Floating System for Phase IV of OC3.pdf”

Please compare the below screenshot with my hand calculations screenshot.

Regarding UnstrLen what i intended to say is, even with usage of stretched length value in UnstrLen of MoorDyn module, after FAST run I am not getting the tension matching with my hand calculation. I did not use MAP++. I was trying to compare the tensions output by FAST and with hand calcs (using catenary equations)

I do agree with your second point that tensions in all mooring lines will not be same for obvious reasons that you and I earlier pointed out.

Please correct me where I could’ve gone wrong in calculations.

Thanks
Vijay

Dear Vijay,

DISTANCE = 848.67 m comes from 853.87 - 5.2 m i.e. the undisplaced radius to the anchor minus the radius to the fairlead from the platform centerline.

Best regards,

Dear Jason,

Many Thanks,
Vijay

Dear Jason,

where can I find the MooringSystemFD.txt for the OC3 Phase IV model you mentioned in your post?

Best regards,

Simon Wiedemann

Dear Simon,

MooringSystemFD.txt is available from the public OC3 folder on Google Drive: drive.google.com/drive/folders/ … VEzT2NjdUk.

Best regards,

Dear Jason,

thank you very much for your fast help.

I am building the OC3 Hywind model in Bladed 4.4. I defined the force-displacement tables for Fx and Fz for horizontal displacements with the files you gave the link to. Are there more values I should define in the Mooring Stiffness matrix?
What to define in the Damping and Mass Matrixes?

I will do free-decay comparison between FAST and Bladed to validate my mooring definition and the other turbine parameters is that the right test?

Best regards,

Simon

Dear Simon,

I’m not sure what you mean when you say, “are there more values I should define in the Mooring Stiffness matrix?”. For planar surge, heave, and pitch motion, Fx, Fz, and My would be important. For full six degree of freedom motion, all six components (Fx, Fy, Fz, Mx, My, and Mz) would be important.

The OC3-Hywind specification does not include a specification of damping or added-mass, so, you could set these to zero in Bladed or make your own assumptions for your own purposes.

Free-decay simulations are always a good place to start. I would look at regular and irregular wave cases.

Best regards,

Dear Jason,

where are the Moments Mx, My, Mz applied to the structure?
As the mooring forces and moments are defined in a plane through the anchor and the fairlead no Fy can be defined.

Best regards,

Simon

Dear Simon,

The loads in MooringSystemFD.txt are expressed in the global inertial reference frame described in section 3 and illustrated in Figure 3-1 of the OC3-Hywind specifications report. Fy can be nonzero for the full mooring system.

It sounds like you may be more interested in the force-displacement curves for an individual mooring line, which are given in MooringLineFD.txt.

Best regards,

Dear Jason,

yes you are right. Sorry for my misspelling.
So how can I get Mx ,My and Mz from MooringLineFD.txt or are Fx and Fz already sufficient in that case?

Best regards,

Simon

Dear Simon,

For an individual mooring line, Fx and Fz are sufficient as they are the forces in the plane of the mooring line, tangent to the line at the fairlead.

Best regards,